Elementary functional analysis /
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| Author / Creator: | MacCluer, Barbara D. |
|---|---|
| Imprint: | New York : Springer, c2009. |
| Description: | 1 online resource (x, 207 p.) : ill. |
| Language: | English |
| Series: | Graduate texts in mathematics ; 253 Graduate texts in mathematics ; 253. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8892354 |
MARC
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| 100 | 1 | |a MacCluer, Barbara D. |0 http://id.loc.gov/authorities/names/n95024129 |1 http://viaf.org/viaf/43544675 | |
| 245 | 1 | 0 | |a Elementary functional analysis / |c Barbara D. MacCluer. |
| 260 | |a New York : |b Springer, |c c2009. | ||
| 300 | |a 1 online resource (x, 207 p.) : |b ill. | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
| 337 | |a computer |b c |2 rdamedia |0 http://id.loc.gov/vocabulary/mediaTypes/c | ||
| 338 | |a online resource |b cr |2 rdacarrier |0 http://id.loc.gov/vocabulary/carriers/cr | ||
| 490 | 1 | |a Graduate texts in mathematics ; |v 253 | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | 1 | |a "This text is intended for a one-semester introductory course in functional analysis for graduate students and well-prepared advanced undergraduates in mathematics and related fields. It is also suitable for self-study, and could be used for an independent reading course for undergraduates preparing to start graduate school." "While this book is relatively short, the author has not sacrificed detail. Arguments are presented in full, and many examples are discussed, making the book ideal for the reader who may be learning the material on his or her own, without the benefit of a formal course or instructor. Each chapter concludes with an extensive collection of exercises." "The choice of topics represents not only the author's preferences, but also her desire to start with the basics and still travel a lively path through some significant parts of modern functional analysis. The text includes some historical commentary, reflecting the author's belief that some understanding of the historical context of the development of any field in mathematics both deepens and enlivens one's appreciation of the subject."--Jacket. | |
| 505 | 0 | |a 1. Hilbert Space Preliminaries -- 1.1. Normed Linear Spaces -- 1.2. Orthogonality -- 1.3. Hilbert Space Geometry -- 1.4. Linear Functionals -- 1.5. Orthonormal Bases -- 1.6. Exercises -- 2. Operator Theory Basics -- 2.1. Bounded Linear Operators -- 2.2. Adjoints of Hilbert Space Operators -- 2.3. Adjoints of Banach Space Operators -- 2.4. Exercises -- 3. The Big Three -- 3.1. The Hahn-Banach Theorem -- 3.2. Principle of Uniform Boundedness -- 3.3. Open Mapping and Closed Graph Theorems -- 3.4. Quotient Spaces -- 3.5. Banach and the Scottish Cafe -- 3.6. Exercises -- 4. Compact Operators -- 4.1. Finite-Dimensional Spaces -- 4.2. Compact Operators -- 4.3. A Preliminary Spectral Theorem -- 4.4. The Invariant Subspace Problem -- 4.5. Introduction to the Spectrum -- 4.6. The Fredholm Alternative -- 4.7. Exercises -- 5. Banach and C*-Algebras -- 5.1. First Examples -- 5.2. Results on Spectra -- 5.3. Ideals and Homomorphisms -- 5.4. Commutative Banach Algebras -- 5.5. Weak Topologies -- 5.6. The Gelfand Transform -- 5.7. The Continuous Functional Calculus -- 5.8. Fredholm Operators -- 5.9. Exercises -- 6. The Spectral Theorem -- 6.1. Normal Operators Are Multiplication Operators -- 6.2. Spectral Measures -- 6.3. Exercises -- Appendix A. Real Analysis Topics -- A.1. Measures -- A.2. Integration -- A.3. L[superscript p] Spaces -- A.4. The Stone-Weierstrass Theorem -- A.5. Positive Linear Functionals on C(X). | |
| 588 | |a Description based on print version record. | ||
| 650 | 0 | |a Functional analysis. |0 http://id.loc.gov/authorities/subjects/sh85052312 | |
| 650 | 4 | |a Mathematics. | |
| 650 | 0 | 7 | |a Funktionalanalysis. |2 swd |
| 655 | 4 | |a Lehrbuch. | |
| 655 | 4 | |a Electronic books. | |
| 655 | 7 | |a Lehrbuch. |2 swd | |
| 650 | 7 | |a Functional analysis. |2 fast |0 http://id.worldcat.org/fast/fst00936061 | |
| 776 | 0 | 8 | |i Print version: |a MacCluer, Barbara D. |t Elementary functional analysis. |d New York : Springer, c2009 |z 9780387855288 |w (DLC) 2008937759 |w (OCoLC)258078575 |
| 830 | 0 | |a Graduate texts in mathematics ; |v 253. | |
| 856 | 4 | 0 | |u http://dx.doi.org/10.1007/978-0-387-85529-5 |y SpringerLink |
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| 035 | |a (ICU)8892354 | ||
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